If you are using
Internet Explorer 10 (or later), you might find some of the links I have used won't
work properly unless you switch to 'Compatibility View' (in the Tools Menu); for
IE11 select 'Compatibility View Settings' and then add this site
(anti-dialectics.co.uk). I have as yet
no idea how Microsoft's new browser,
Edge, will handle these links.

For some reason I can't
work out, Internet Explorer 11 will no longer play the video I have posted to
this page. Certainly not on my computer! However, as far as I can tell, they
play in other Browsers.

Anyone using these links must remember that
they will be skipping past supporting argument and evidence set out in earlier
sections.

If your Firewall/Browser has a pop-up blocker, you will need to press the
"Ctrl" key at the same time or these and the other links here won't work!

I have adjusted the
font size used at this site to ensure that even those with impaired
vision can read what I have to say. However, if the text is still either too
big or too small for you, please adjust your browser settings!

I have
posted many similar comments on other pages at YouTube that are devoted to this
theory and received little or no response. But, the producer of this film
(whose on-screen name used to be Marxist-Leninist-Theory [MLT], but which has now changed
to The Finnish Bolshevik -- henceforth, TFB) did respond (and to which
I replied, here and
here).

[All my debates and responses to TFB have now been
collected together,
here.]

Not long
afterwards, another video appeared on YouTube, which was also produced by MLT (but posted
to his other site) -- entitled: "Refuting
a Trotskyite Attack on Dialectics" -- although after being asked to drop the
derogatory term "Trotskyite", MLT has agreed to stop using it:

Video
One: The 'Case' For The Prosecution

After
having viewed this video, it is quite clear that it closely resembles the
attempts made by several others who have tried to show that my work is
thoroughly misguided, if not mendacious (I will highlight the basic errors of
interpretation that litter this production as this response unfolds), and it
succeeds about as much as all the rest have, too -- , i.e., not even close!

However,
this video is unlike the other responses MLT has thought to make in that it
contains down-right lies about my ideas. [There is no other word I can
think of that better describes MLT's new tactic -- as the reader will soon see
for herself.] They will also be exposed as this response progresses.

As I note
on the opening page of my site (referring readers to a page where I have listed most of
the attempts made by DM-supporters to challenge my work):

The above page contains links to forums on the web where I have 'debated' this creed
with other comrades. For anyone
interested: check out the desperate 'debating' tactics used by Dialectical
Mystics in their attempt to respond to my ideas. You
will no doubt notice that the vast majority all say the same sorts of things, and
most of them pepper their remarks with scatological and abusive language. They
all like to make things up, too, about me and my beliefs.

[I have now added MLTs video as a
particularly egregious example of the lies DM-fans are prepared to spin.]

30
years (!!) of this stuff from Dialectical Mystics has meant I now take an
aggressive stance toward them every time -- I soon learnt back in the 1980s that
being pleasant with them (my initial tactic) didn't alter by one jot their abusive tone,
their propensity to fabricate, nor reduce the amount of scatological language
they used.

MLT's
language seems not to have descended to this level (yet!), but he certainly
follows a well-trodden DM-path of preferring to make stuff up about my work in
order to 'take down' a straw man.

~~~~~~oOo~~~~~~

I had
wanted this reply to be confined to one page only, but MLT has included new
criticisms of my work not contained in his other responses. Unfortunately, this has meant that
my reply will once more stretch over several pages! Indeed, in order to
do justice to this video (it is after all over 40 minutes long!), anything less
would be an insult.

[I have also included a
word-for-word transcript of this somewhat garbled
and repetitive video, which has alone added at least 15-20% to the length of this
response.]

(1) MLT
assumes my attack on this theory is an attack on Marx, Engels and Lenin (I have
omitted Stalin and Mao's names here since, as a Trotskyist, I do not hold them
in any esteem -- quite the opposite, in fact), but he neglected to quote me to this effect. Indeed, I say the
opposite (and at the very beginning of the Introductory Essay which is the main
focus of this video):

Nothing said below
is aimed at undermining Historical Materialism
[HM] -- a theory I fully accept -- or, for that matter, revolutionary socialism. My aim is
simply to assist in the scientific development of Marxism by helping to demolish a
dogma that has in
my opinion seriously
damaged our movement from its inception: Dialectical Materialism
[DM] -- or, in its more political form, 'Materialist Dialectics' [MD].

Naturally, these are highly controversial allegations,
especially since they are being advanced by a Marxist;
the reason
why I am publishing them is partially explained below, and in far more detail in my
other
Essays. Exactly why I began this project is explained
here.

Some readers might wonder how I can claim to be both a Leninist and a
Trotskyist given the highly critical things I have to say about philosophical ideas that
have been an integral part of these two traditions from their inception. However, to
give an analogy: we can surely be highly critical of
Newton'smysticalideas
even while accepting the scientific nature of his other work. The same
applies here.

I count myself as a Marxist, a Leninist and a Trotskyist
since I fully accept, not just HM (providing
Hegel's baleful influence has been fully excised), but
the political ideas associated with the life and work of Marx,
Luxembourg, Lenin and Trotsky. Some might think that this must compromise HM
itself, in that HM would then be like a "clock without a spring". The reverse is the case. As I
aim to show
below: if DM were true,
change would in fact be impossible.

[MLT
attempts, somewhat sarcastically, to malign me for the words I posted in the
first paragraph; I will deal with his comments in Part Two.]

In which
case, this
is no more a personal attack on Marx, Engels or Lenin than would be a
similar criticism of Newton for allowing mystical ideas to corrupt his
scientific work. Nor is this an attempt to show that Marx, Engels and Lenin were
completely wrong (or "idiots" to use MLT's term --
this is a class,
not an individual, issue).

For one thing, as is relatively easy to show,
Marx didn't
accept this theory, and had abandoned Philosophy root-and-branch by the late
1840s. [On that, see
here, here,
and
here.] For another, as I note above, I am in 100% agreement with Marx,
Engels and Lenin over the nature of revolutionary socialism, and since these
three great revolutionaries wrote far more on that particular subject than they ever
devoted to DM, this means I am in agreement with the vast bulk of their work.

[One of
the problems arguing with DM-supporters is that they tend to skim read my
work looking for things to attack, and that means they almost invariably
miss key parts of it, which then, naturally, prompts them into mis-interpreting what they
think they have read. It looks like MLT has
done this, too. Indeed, we will see him do precisely this many times over as this reply
unfolds, which error, in his case, has been compounded by an unwise propensity to
tell (easily exposed) fibs.]

(2) MLT
confuses my claim to have demolished DM with what he interprets as arrogance on my
part:

In fact, as I also note elsewhere, my
demolition depends as much on Marx's own ideas as it does on that of others,
to whom
I give credit at every turn. The only originality in my work lies in (a) the
use to which I have put these ideas, (b) their mode of presentation and (c) my
endeavour to keep as much of my work as possible accessible to those with little
or no knowledge of technical issues. That is why I asserted that this was a
demolition from a "Marxist angle", not my own! I claim Marx's authority
as the main inspiration for my Essays. MLT might find this particular point risible, but it is based on Marx's own
words, and for these reasons:

(a) My
work is
systematically and consistently anti-philosophical, as was Marx's:

"Feuerbach's
great achievement is.... The proof that philosophy is nothing else but
religion rendered into thought and expounded by thought, i.e., another form
and manner of existence of the estrangement of the essence of man; hence equally
to be condemned...." [Marx
(1975b), p.381. I have used the on-line version, here. Bold emphasis
and link added.]

"One has to 'leave philosophy aside'..., one has to leap out of it and devote
oneself like an ordinary man to the study of actuality, for which there exists
also an enormous amount of literary material, unknown, of course, to the
philosophers." [Marx
and Engels (1976), p.236. Bold emphasis added. Quotation marks altered to
conform to the conventions adopted at this site.]

(b) It
re-directs our attention to ordinary, as opposed to philosophical language,
again taking its cue from Marx:

"One of the most difficult tasks confronting
philosophers is to descend from the world of thought to the actual world.
Language is the immediate actuality of thought.Just as
philosophers have given thought an independent existence, so they were bound to
make language into an independent realm. This is the secret of philosophical
language, in which thoughts in the form of words have their own content. The
problem of descending from the world of thoughts to the actual world is turned
into the problem of descending from language to life.

"We have shown that thoughts and ideas acquire an
independent existence in consequence of the personal circumstances and relations
of individuals acquiring independent existence. We have shown that exclusive,
systematic occupation with these thoughts on the part of ideologists and
philosophers, and hence the systematisation of these thoughts, is a consequence
of division of labour, and that, in particular, German philosophy is a
consequence of German petty-bourgeois conditions. The
philosophers have only
to dissolve their language into the ordinary language, from which it is
abstracted, in order to recognise it, as the distorted language of the actual
world, and to realise that neither thoughts nor language in themselves form a
realm of their own, that they are only manifestations of actual life."
[Marx
and Engels (1970), p.118. Bold emphases alone added.]

And there
are excellent reasons for doing this, too, over and above Marx's clear advice -- on that,
see here and
here.

(3) MLT
has concentrated his attention on an introductory work of mine -- indeed, I
emphasised this point at the
top of the
Essay in question:

Please note that this Essay deals with very basic issues, even at the risk of
over-simplification.

It has only been ventured upon because
several comrades (who weren't well-versed in Philosophy) wanted a
very simple guide to my principle arguments against DM.

In that case, it isn't aimed at
experts!

Anyone who objects to the
apparently superficial nature of the material presented below must take these
caveats into account or navigate away from this page. The material below isn't intended for them.

It is worth underlining this point since
I still encounter comrades on Internet discussion boards who, despite the above
warning, still think this Essay is a definitive statement of my ideas. It isn't!

Any who still find this Essay either too
long or too difficult might prefer to read two much shorter summaries of my
ideas: here and
here.

Attempting to 'refute' my attack on DM using only (or mainly) the above Essay
would be like trying to refute Das Kapital by concentrating solely on
Wage Labour and Capital!

[Not at I
am comparing myself to Marx! The point is that if comrades want to refute my
work, they should concentrate on the core Essays, not work aimed at novices!
Indeed, MLT makes the mistakes he does simply because he hasn't
done this. By way of contrast, I have consulted (and studied, many
times), stretching over several decades, the work of the DM-classics and
countless 'lesser' DM-works. Anything less than this would be to treat Marx,
Engels, Lenin and all the rest with contempt.]

I have
also listened to and watched the above video many times over -- not only
in order to transcribe it as accurately as I can, but also in order to do
justice to MLT's criticisms.

MLT
says he hasn't the time or inclination to read my work -- fine, no one is forced
to read anything I have written. But, only a fool would presume to attack
another's work based on approximately 2% of it (my site now stretches to
well over 2.75 million words -- the Essay in question is approximately 43,500
words long), and it's an Essay aimed only at novices, too!

(4)
Although this doesn't feature as part of his 'refutation', MLT laments the
fact that my site is rather difficult to navigate around, and he seems to
connect this with all the links I have inserted (which take to reader to other Essays, and
around in a circle sometimes).

Well, it
is rather odd being criticised by a DM-supporter for linking things when it
seems to be a fundamental DM-thesis that everything is interlinked!

However, one of the reasons I have done this is to help
prevent readers from drawing the wrong conclusions about my work. Since
it isn't possible (or even desirable) to make every single point one should like
to make, or list all the caveats one would like to include, in a single sentence
or paragraph, I have had to link many of the things I assert to other parts of
my work where I have either argued the point more fully, or have supplied the
necessary evidence in support of whatever it is that I had said. As we will
see, MLT clearly failed to follow many of these links, and hence advanced numerous false
or misleading accusations about my ideas (examples will be given
below).

And sure,
my site isn't easy to follow, but here is the reason why (this comes from the
opening page of my site):

These Essays represent work in progress; hence they do not
necessarily reflect my final view.

I am only publishing this material on the Internet
because several comrades whose opinions I respect urged me to do so back in 2005
-- even though
the work you see before you is less than half complete. Many of my ideas are still in
the formative stage and need
considerable
attention devoted to them to
mature.

I estimate this project
will take another ten years to complete before it is fit to publish either here
in its final form or in hard copy.

All of these Essays will have radically
changed by then.

This work
will be updated regularly -- edited and re-edited
constantly --, its arguments clarified andprogressivelystrengthened as my
research continues (and particularly as my 'understanding' of Hegel develops).

So, visitors are encouraged to check back often.

It is
because this work appeared long before I considered it ready that it is in the
state it is. Hence, in its present form it more closely resembles a
Rube Goldberg machine than it does a finely-tuned Ferrari -- this also partially explains all those links
(which hold the site together like sticking plaster!) -- a 'machine' cobbled together in a
piece-meal fashion over the last ten years. I can only apologise to the reader
for this, but there was no way round it given the above considerations.

About 3
minutes into the video, MLT attempts to tackle a subject about which he claims
not to be an expert: FL -- whereas I have a mathematics degree, and have studied
logic to postgraduate level. I say this neither to brag nor to 'pull rank',
but I am heartily tired of being told what is or is not the case with respect
to FL by
those who seem to know very little about it, but who could have easily found out
(on-line) that what they had to say about FL in fact became obsolete over 140
years ago. Indeed, much of it was obsolete when Aristotle was alive!

"Formal categories, putting
things in labelled boxes, will always be an inadequate way of looking at change
and development…because a static definition cannot cope with the way in which a
new content emerges from old conditions." [Rees (1998), p.59.]

"There are three fundamental laws of formal
logic. First and most important is the law of identity....

"…If a thing is always and
under all conditions equal or identical with itself, it can never be unequal or
different from itself." [Novack
(1971), p.20.]

However, I
have yet to see a single quotation from a logic text (ancient or modern) that supports
these allegations
-- certainly dialecticians have so far failed to produce even so much as one.

And no wonder; they are
completely false.

FL uses
variables
-- that is, it employs letters to stand for propositions, objects, processes and the like,
all of which can and do change.

This handy formal device was invented by the very first logician we know of (in the
'West'),
Aristotle (384-322BC). Indeed, Aristotle experimented with
the use of variables approximately 1500 years before they were imported into mathematics by
Muslim
Algebraists, who in turn employed them several centuries before
French mathematician and philosopher,
René
Descartes (1596-1650), introduced them into the 'West'.

Engels himself said the following about that particular innovation:

"The turning point in mathematics was Descartes'
variable magnitude. With that came motion and hence dialectics in mathematics,
and at once, too, of necessity the differential and integral calculus…." [Engels
(1954), p.258.]

Now, no one doubts that modern mathematics can
handle change, so why dialecticians deny this of FL -- when it has always used variables
-- is
somewhat puzzling.

But, in
the clip showing the section of the Essay in question, the viewer can clearly
see a link to another page at my sitewhere I do precisely this -- Essay
Four Part One! So, the above
quotation from this video should now be altered to read (more honestly) as follows:

"I made no
attempt to find out how Ms Lichtenstein explains how Formal Logic deals
with change. The onerous task of clicking on a link was far too much effort for me!"

MLT now
switches into full sarcasm mode:

"I for one can't
figure it out.... I guess our Trotskyite revisionist has some brilliant theory
about this which is just beyond the minds of us mere mortals..." [Approx 04:19.]

1) I
don't have a theory; nor do I want one (which is a point I made in the
Introductory Essay to my site).

Indeed,
we don't need one (on why that is so, see Essay Twelve
Part One). All it would take for
MLT (and his happy band of 'mere mortals') to grasp this simple point is: click on a link, read a few sections
of Essay Four Part One, and all will become clear to him/them.

2) Anyway,
what is so wrong with 'revisionism'?

Were the DM-classicists infallible? Were
they possessed of semi-divine wisdom, so that they never, ever made a
theoretical or factual mistake? Or never, ever lacked sufficient information to develop an informed
opinion?

If,
according to Lenin, human knowledge isn't absolute, but relative
and incomplete, then this must also be true of DM. Or was Lenin wrong? Does the
only absolute knowledge in existence belong to Marxist-Leninist parties?

Has (genuine) science changed at all in the last two millennia? If it has, why
can't DM change?

How
come the only thing in the entire universe not subject to change is DM itself?

Relying
on memory alone, and hence failing to quote me on this (however, what I
said is easy to find;
here it is), MLT now tries to make a point in response to something I said
on a different YouTube page:

"...They argue
that modern temporal logic, for example, copes with change rather well.... So,
judging from this talk about math and temporal logic I think this person
misunderstands what people mean when they say formal logic can't handle change.
It's not that some change cannot be represented in terms of formal logic -- for
example, you can use time as a variable and then say, for example, 'Now A is x
and after one hour A is y', or something like that [sic!] -- however, that
doesn't change the fact that this is purely theoretical, that these are only
static objects that have no connection to reality, whereas things in the real
world are interconnected and being affected by each other, changing and creating
change elsewhere, almost as if they were in a dialectical relationship [said
with a slightly funny voice! -- RL]. What do you know! That said, even if the
claims of this Trotskyite were true...it still wouldn't be an argument against
dialectics, because it's only a defence of formal logic." [Approx 05:03-06:08.]

Well,
there are nearly as many errors and misconceptions in the above as there are
words.

1) In
fact, there was no misunderstanding on my part, since DM-theorists themselves
are entirely unclear what they mean when they tell us FL can't cope with
change, just as they are even less clear how their own theory manages to do the
opposite of this. The very best they can do is assert (again, without even a
cursory attempt to provide any evidence) that FL deals with "static" objects -- when,
of course, it deals with no objects (or concepts) at all!

We can
see this confusion in miniature form in the above comments. After telling us (or
rather, after summarising something MLT substituted for TL,
not having checked what that branch of logic actually has to tell us -- his "something like that" is
the
give-away, here!) -- after telling us that TL focuses on sentences like, "Now A is x and after one hour A is
y" (all the while failing to inform us what these letters stand for, thus following on in
yet another well-established DM-tradition of posting garbled schematic sentences as
supposed examples of FL/TL! -- on that, see
here), he then
informs us that "these are only static objects", when he has just shown
us they
change! "A used to be x, now it is y". Is this an example of change
or not? It sure looks like
one. This perhaps tells us that MLT doesn't actually know what a "static
object" is (in FL or anywhere else, perhaps).

2) As
noted above, MLT's in depth research into TL amounted to...making up a
sentence supposedly drawn from it. [What was that I said earlier about
dialecticians telling fibs about FL? The very idea!] There are plenty of sites
on the Internet that would have told him what TL is.
Here
is one, and
here
is another -- and, of course,
there is
always good old
Wikipedia.

3) Next,
MLT informs us that these TL-sentences are "purely theoretical", and "have no
connection to reality". Now, it might come as a surprise to, say, Physicists,
that they, too, have a theory -- called Relativity [RT] -- that it is "purely
theoretical" and thus has "no connection to reality".

"Not
fair!" I hear someone say. "RT does deal with processes in
the real world, so it isn't 'purely theoretical'". Indeed, but that is only when
the Pure Mathematics and the Theoretical Physics (in which RT is usually
expressed) have been
interpreted, and then re-shaped as a series of "real world" models. Left as
uninterpreted Pure Mathematics and Theoretical Physics, RT would suffer
from all the supposed/alleged 'weaknesses' of FL/TL.

Here is
how I have addressed this issue in Essay Four Part One:

Despite this, does the charge that FL can't cope with
change itself hold water? In order to answer this question, consider a valid
argument form taken from Aristotelian Formal Logic [AFL]:

L1: Premiss 1: No As are B.

L2: Premiss 2: All Cs are B.

L3: Ergo: No As are C.

In this rather uninspiring valid argument
schema the conclusion follows from the premisses no matter what legitimate
substitution instances replace the variable letters. [Examples are given in the
Footnote reproduced below.]

So, L3 follows
from the premisses no matter what. But, the
argument pattern this schema expresses
is transparent to change: that is, while it can cope with change, it takes no stance on
it (since it is comprised of schematic sentences that are incapable of being
assigned a
truth-value until they have been interpreted). Some might regard this as a serious drawback, but this is no more a failing
here than it would be, say, for Electronics to take no stance on the evolution
of Angiosperms (even
though electronic devices can be used to help in their study). Otherwise, one might
just as well complain that FL can't predict the
weather or eradicate
MRSA.

What FL
supplies us with are the conceptual tools that enable us to theorise about change.

Moreover,
the
truth-values of each of the above schematic sentences depend on the
interpretation assigned to the variables (i.e., "A", "B" and "C"). The premisses
of L1 aren't actually about anything until they have been interpreted;
before this has been done they are neither true nor false. Not only that,
but the indefinite number of ways there are of interpreting schematic letters
like those in L1 means that it is possible for changeless and changeable
items to feature in any of its concrete instances.

[That was the point behind the
observation
made earlier that dialecticians and logical novices often confuse validity
with truth; the above schema is valid, but its schematic propositions can't be true or false, for obvious reasons.]

To illustrate the absurdity of the idea that
just because FL uses certain words or letters it can't handle change (and uses
nothing but 'rigid' terms), consider this parallel 'argument':

(1) If x = 2 and f(x) =
2x + 1, then if y = f(x), y = 5.

(2) Therefore x and y
can never change or become any other number.

No one would be foolish enough to argue this
way in mathematics since that would be to confuse variables with constants. But,
if this is the case in mathematics, then DM-inspired claims about the alleged
limitations of FL seem all the more bizarre -- to say the least.

Of course, it would be naïve to suppose that
the above considerations address issues of concern to DM-theorists. As John Rees points out:

"Formal categories, putting
things in labelled boxes, will always be an inadequate way of looking at change
and development…because a static definition can't cope with the way in which a
new content emerges from old conditions." [Rees (1998), p.59. Added on
edit: I have quoted this since Rees and MLT agree on this point, as do many
other DM-supporters, whether they are Trotskyists, like Rees, or Stalinists or
Maoists.]

But, as a criticism of
FL, this is entirely misguided. FL doesn't put anything in "boxes", and
its practitioners don't deny change as a result. DM-theorist have yet to quote a
single textbook of logic (other than Hegel's!) that supports this allegation.

Added in
a footnote:

With respect to this argument schema, the only condition
validity requires is the following: if, for a given interpretation, the
premisses are true then the conclusion is true. That claim isn't affected by the fact that schematic premisses themselves can't be
true or false, since such schema express rules, and are hypothetical. [A clear explanation
of this can be found
here.]...

The above syllogism is valid, and would remain valid even
if all motion ceased. But, it also 'copes' with movement (and indeed
with all types of movement), and hence with
change, as is clear from what it says.

And we don't have to employ what seem to be
'necessarily true' premisses (or, indeed, this particular argument form) to make the point:

Premiss 1: All human beings
are aging.

Premiss 2: All Londoners are
human beings.

Ergo: All Londoners are aging.

Admittedly, the term "aging" isn't of the
type Aristotle would have countenanced in a syllogism (so far as I can
determine). However, if we free
Aristotle's logic from his metaphysics, and adjust the formation rules slightly, the inference is clearly valid, and
based on a syllogistic form. Anyway, the term "aging" can easily be replaced by
a bona fide universal term (such as "the class of aging animals"), to
create this genuine, but stilted, syllogism:

Premiss 1: All human beings
are members of the class of aging animals.

Premiss 2: All
Londoners are human beings.

Ergo: All Londoners are members of the class of aging animals.

[Except, of course, Aristotle would have
employed "All men" in place of "All human beings".]

Finally, here is an argument that depends on change:

Premiss 1: All rivers flow to the sea.

Premiss 2: The Mississippi is a
river.

Ergo: The Mississippi flows to the sea.

A couple of points are worth making about the
above argument:

1) In order for the conclusion to follow, the
premisses of an argument do not have to be true -- clearly Premiss 1 is false.

2) The above argument isn't of the
classic syllogistic form, although it parallels it.

3) Anyone who understands English will
already know that rivers are changeable, and that they flow; this example
alone shows that logic can not only cope with changeable 'concepts', it actually
employs them. Hence, logic is capable of utilising countless words that express
change in a far more varied and complex form than anything Hegel (or his
latter-day DM-epigones) ever imagined. [On that, see
here.]

Here is another example:

Premiss 1: All fires release heat.

Premiss 2: I have just lit a fire.

Ergo: My fire will release heat.

Or,
even:

Premiss 1: All sound waves transmit
energy.

Premiss 2: Thunder is a sound wave.

Ergo: Thunder transmits energy.

The
above examples are perhaps more akin to argument forms found in
Informal Logic, but that is also true of most interpretations of argument
forms drawn from FL, too.

To be sure, the above changes aren't of the sort that interest dialecticians, but, as I note in the main body of this
Essay, examples like this have only been quoted to refute the claim that FL
can't cope with
change. Combine that idea with the additional thought that dialectics itself can't
cope with change itself (on that, see
here),
and the alleged 'superiority of DL over FL turns into its own opposite.
Which is yet another rather fitting 'dialectical inversion'.

[DL = Dialectical Logic; MFL = Modern Formal Logic.]

Some
might object that while the above examples might appear to cope with some
changes in reality, but they ignore conceptual change, and as such show once
again that FL is inferior to DL. I deal with conceptual change
later in this Essay.

There is an excellent account of Aristotelian
Logic in
Smith (2015). And there is an equally useful account of
MFL (i.e., now
confusingly called "Classical Logic") in
Shapiro (2013).

In the
above, I specifically chose an example drawn from
AFL to show that even it could
cope with change; had I employed all the techniques available to us in
MFL, it would have become even clearer how FL more easily copes with change.
[Readers are directed to Essay Four Part
One for more details.]

Also from
Essay Four Part One:

Of even greater significance is the fact that
over the last hundred years or so theorists have developed several post-classical
systems of logic, which include
modal,
temporal,
deontic,
imperative,
epistemic and
multiple-conclusion logics
(among others). Several of these systems sanction even more sophisticated
depictions of change than are allowed for in AFL, or even MFL....

The details of these other systems of
Logic can be found in Goble (2001), Hughes and Cresswell (1996), Haack (1978, 1996), Hintikka
(1962), Jacquette (2006),
Prior (1957, 1967, 1968) and Von Wright (1957, 1963). A general survey
of some of the background issues raised by Classical and Non-Classical Logic can
be found in Read (1994). In fact, Graham Priest (who is both a defender of
certain aspects of dialectics, and an expert logician) has written his own admirable
introductions; cf., Priest (2000, 2008). Also worth consulting are the following:

Despite this embarrassment of riches, freely
available on the internet, DM-fans stoutly cling to their
studied ignorance, maintaining their self-inflicted
nescience while pontificating about
the alleged limitations of FL, as if each one
were a latter-day
Aristotle. [Anyone who doubts this need only examine, say, Trotsky's lamentably
poor 'answer' to
James
Burnham, in Trotsky (1971),
pp.91-119;
196-97,
232-56. See also,
here
and here.]

The point
is that when we supply the formal schemas studied in
MFL (or even in AFL) with an interpretation -- just
as we do in Physics -- those schemas do in fact relate to the "real world" --
contradicting MLT.

Hence,
once they have been interpreted, these terms can (and often do) express change.

This
means that what MLT alleges of FL is misguided in the
extreme. [Well, he did say he wasn't an expert!]

[It is important to note that "Interpretation"
doesn't mean the same in logic as it does in the vernacular; it relates to the
substitution instances that result from the systematic replacement of
variable letters with what they supposedly mean (often these are derived from ordinary
language, but they can also be taken from scientific or mathematical languages), according to the syntax and/or
the semantics of formal system involved.]

4) My
argument wasn't a defence of FL; FL needs no more defending than mathematics
does. It was aimed at showing that DM-theorists and supporters make things up
about FL and they do so from a position of almost total ignorance, repeating the same things
they have uncritically picked up from one another, or have read in other books on DM (which were similarly supported by
not one single
quotation from an FL-textbook) -- as we have seen is the
case with MLT.

Earlier
in the video (at approximately 03:35), MLT asserted that logic is different
from mathematics. This was aimed at countering the analogy I drew between the
variables used in FL and the variables used in Mathematics. Well, this argument
might have carried some weight (but very little) two hundred years ago, but it
carries none at all since the revolution in MFL that took place 140 years ago
(with the work of
Frege).
As a result, we now have a thriving discipline called
Mathematical Logic [ML]. Naturally, this discipline can cope with change
just as
well as Mathematics can.

MLT's
next point concerns the alleged contradictory nature of motion -- a dogmatic
idea DM-theorists have imported into Marxism from the speculative theories of
assorted Idealists and Mystics, in support of which there isn't a shred of
physical evidence -- just a few trite, badly-worded, verbal arguments (compounded by
the use of garbled concepts drawn from 18th
century calculus).

[MLT
seems to have a problem with my accusation that Engels, Lenin, Mao and Stalin
(but, note, not Marx) adopted and then promoted a "dogmatic" theory --
DM. In fact, not two weeks after making the above video, he posted another
entitled "Dogmatism
in Marxism". I will deal with that 'issue' in Part Two.]

So, what
does MLT have to say? First of all he attempts to summarise
Zeno's
argument for the impossibility of motion, and he then adds:

"Our Trotskyite
brings up this paradox, and roughly..., you know, explains it, but doesn't really
deal with it in any way; but just points out 'Oh, this is a paradox, blah, blah,
blah.... Therefore something....'" [Approx 07:46.]

Ok, so
let's see how accurate the above 'summary' of my argument is; here is what I
actually wrote (a small fraction
of which was posted on-screen in the video) itself:

This is an age-old confusion derived from a
paradox
invented by an Ancient Greek mystic called
Zeno (490?-430?BC).

In fact, as should seem obvious, all objects (which aren't mathematical points)
occupy several places at once, whether or not they are moving. So, for example, while you are sat reading this
Essay your body isn't compressed into a tiny point! Unless you have suffered
an horrific accident, your head won't be in exactly same location as your
feet, even though both of these body parts now (pre-accident!) occupy the same place -- i.e., where
you are sat. So, occupying several points at the same time isn't unique
to moving bodies. In which case, this 'paradox' has more to do with linguistic
ambiguity than it has with anything
'contradictory'. [The
ambiguity here is plainly connected with words like "place" and "location",
the meanings of which Engels seems to think are perfectly obvious; more on that presently.]

Notice, I
nowhere try to "explain" this paradox, so I am not too sure what the above
"Blah, blah, blah" is all about. And, can anyone see a "Therefore something" in the
above?

As seems
clear, DM-supporters don't just tell fibs about FL.

But, am I allowed to be
this cavalier with MLT's words in return?

I think
not...

MLT
then refers his viewers to
another page (over at the Soviet Empire Forum), where another comrade attempted to refute my case against DM,
after which MLT states:

"The interesting
thing here is that the comments exchanged [MLT's words aren't clear here - RL]
that is cited doesn't actually fare too favourably for the Trotskyite. The
person challenging them gives a completely sufficient refutation of their
arguments to which they don't respond with anything, and instead just, you know,
just gloat here to have demonstrated how this theory apparently leads to 'even
more ridiculous conclusions'. So, the refutation that the person challenging our
Trotskyite's views [again this part isn't too clear -- RL] is based on Physics
and is the following (also got to love the fact that (garbled) the explanation
by this Trotskyite...they're so vague, it's like...couple, multiple times it
seems like they're just saying 'Oh, this is a contradiction, therefore it's
wrong', even though, of course, it's a contradiction, that's the whole
point...):

'when a body is
in motion its velocity is not zero and therefore...v = dx/dt =/= 0

'What we’re
discussing are fundamental facts of physics which you have to understand prior
to attempting to understand philosophical theories involving them....

'During motion, the position of a body in physical terms is defined by x and yet
it is not defined by x but is defined by dx. When in motion a body is at one
point x and yet it is at two points whose difference is dx. The same applies to
time -- you can define the body in motion at time t and yet there is a
difference of two times, dt, which also characterizes temporally a body in
motion. These are obviously contradictory conditions of motion, coexisting.
Motion is a constant resolution of these contradictions. This is what physics
says....'

"And the
Trotskyite counter-argument is...seems to be..., er... 'This is silly, hah hah
hah' ..., like, that's not an argument. 'Yeah, I mean, physics is kind of funny
sometimes', that's not an argument. The rest of their counter-arguments are just
silly. Instead of contesting the fact that things in motion exist in multiple
places at the same time, they turn around and argue that really all physical
bodies exist in multiple places, for example, beans exist inside a tin and
inside a store. or your head and your feet exist in different places despite
being your body. However, this is simply word-play. The point they're making is
that things don't exist in a single point but in an area, but that has no impact
on the argument whatsoever on Engels nor anyone that the Trotskyite is arguing
against has (sic) ever claimed that humans, beans or tin cans exist in a single
point. It's obvious that wasn't what Engels was arguing about. Besides, this kind
of talk is metaphysical. And then they proceed to say that 'You know, this is
an...um.., mistake by Engels because this kind of idea applies to things that are
not in motion, for example, you know..., beans in tin cans.' But as I just
pointed out, that's not what Engels was talking about at all because, yeah...,
well, you get the point. It's just, er..., word games to say 'Oh, beans exist
inside a tin can inside a warehouse...,' that's.. obviously it's not the same
location, it's not the same point existing inside a tin and also inside a
factory or a warehouse, whatever, doesn't mean they exist in two different
points." [Approx 07:50-11:50.]

Once
again, there are nearly as many errors in there as there are
words.

1)
However, I am genuinely amazed by the blatant lies in the above passage! Did
MLT
imagine that no one would check my answers to the critic he
quoted -- while he [MLT] failed to quote (or summarise) any of my responses? Did he honestly
think that when others read what I posted they would summarise my words as
follows: "This is silly, hah hah hah"? In
fact, I rather suspect he was hoping no one would visit the Soviet Empire Forum
and check this for themselves -- and from the comments posted below this video, it
looks like he was right; no one bothered to check his downright lies!

Ok, so
here is part of what I posted in reply to this individual (who wrote under the
name 'Future World' [FW]) -- see if you think any of it amounts to "Yeah, I mean,
physics is kind of funny sometimes!" -- or even "This is silly, hah hah hah":

Well, this
isn't my objection (and
I note you do not quote me to this effect). My objection is far more complex
than this. Here, in fact, is just
one of my core
objections to Engels and Hegel:

From this point on
it will be assumed that the difficulties with Engels's account noted in the
previous section can be resolved, and that there exists
some way of reading his
words that implies a contradiction, and which succeeds in distinguishing moving
from motionless bodies.

Perhaps the following will suffice:

L10: For some body b, at some time t, and for two places p and q, b is at p at t
and not at p at t, and b is at q at t, and p is not the same place as q.

This looks pretty contradictory. With suitable conventions about the use of
variables we could abbreviate L10 a little to yield this slightly neater
version:

L11: For some b, for some t, for two places p and q, b is at p at t and not at p
at t, and b is at q at t.

This latest set of problems revolves around the supposed reference of the "t"
variable in L11 above.

It's always possible to argue that L11 really amounts to the following:

L12: For some b, during interval T, and for two 'instants' t1 and t2 [where both
t1 and t2 belong to T, such that t2 > t1], and for two places p and q, b is at p
at t1, but not at p at t2, and b is at q at t2.

[In the above, t1 and t2 are themselves taken to be sets of nested
sub-intervals, which can be put into an isomorphism with suitably chosen
intervals of real numbers; hence the 'scare' quotes around the word "instant" in
L12.]

Clearly, the implication here is that the unanalysed variable "t" in L11
actually picks out a time interval T (as opposed to a temporal instant) --
brought out in L12 -- during which the supposed movement takes place. This would
licence a finer-grained discrimination among T's sub-intervals (i.e., t1 and t2)
during which this occurs. Two possible translations of L12 in less formal
language might read as follows:

L12a: A body b, observed over the course of a second, is located at point p in
the first millisecond, and is located at q a millisecond later.

L12b: A body b, observed over the course of a millisecond, is located at point p
in the first nanosecond, and is located at q a nanosecond later.

And so on…

Indeed, this is how motion is normally conceived: as change of place
in time -- i.e., with
time having advanced while it occurs. If this were not so (i.e., if L12 is
rejected), then L11 would imply that the supposed change of place must have
occurred outside of time
-- or, worse, that it happened
independently of the passage of time --, which is either
incomprehensible, or it would imply that, for parts of their trajectory, moving
objects (no matter of how low their speed) moved with an
infinite velocity! This
was in fact pointed out earlier.

And yet, how else are we to understand Engels's claim that a moving body is
actually in two places at once? On that basis,
a moving body would move from
one place to the next outside of time -- that is,
with time having advanced not
one instant. In that case, a moving body would be in one place at one
instant, and it would move to another place with no lapse of time; such motion
would thus take place outside of time (which is tantamount to saying it does not
happen, or does not exist).

Indeed, we would now have no right to say that such a body was in the first of
these Engelsian locations before it was in the second. [That is because "before"
implies an earlier time, which has just been ruled out.] By a suitable induction
clause, along the entire trajectory of a body's motion it would not, therefore,
be possible to say that a moving body was at the beginning of a journey before
it was at the end! [The reasons for saying this will be provided on request.]

Despite this it would seem that this latest difficulty can only be neutralised
by means of the adoption of an implausible stipulation to the effect that
whereas time is not composed of an infinite series of embedded sub-intervals --
characterised by suitably defined nested sets of real numbers --,
location is.

This would further mean that while we may divide the position a body occupies as
it moves along as finely as we wish -- so that no matter to what extent we slice
a body's location, we would always be able to distinguish two contiguous points
allowing us to say that a moving body was in both of these places at the same
time --, while we can do that
with respect to location, we cannot do the same with respect to time.

Clearly, this is an inconsistent approach to the divisibility of time and space
-- wherein we are allowed to divide one of these (space) as much as we like
while this is disallowed of the other (time). [It could even be argued that this
is where the alleged 'contradiction' originally arose -- it was introduced into
this 'problem' right at the start by this inconsistent (implicit) assumption, so
no wonder it emerged at a later point -- no puns intended.]

This protocol might at first sight seem to neutralise an earlier objection
(i.e., that even though a moving body might be in two places, we could always
set up a one-one relation between the latter and two separate instants in time,
because time and space can be represented as equally fine-grained), but,
plainly, it only achieves this by stipulating (without any justification) that
the successful mapping of places onto (nested intervals of) real numbers (to
give them the required density and continuity) is denied of temporal intervals.

So, there seem to be three distinct possibilities with these two distinct
variables (concerning location and time):

(1) Both time and place are infinitely divisible.

(2) Infinite divisibility is true of location only.

(3) Infinite divisibility is true of either but not both (i.e., it is true of
time but not place, or it is true of place but not time).

Naturally, these are not the only alternatives, but they seem to be the only
three that are relevant to matters in hand.

Of course, one particular classical response to this dilemma ran along the lines
that the infinite divisibility of time and place implies that an allegedly
moving body is in fact at rest at some point; so, if we could specify a time at
which an object was located at some point, and only that point at that time, it
must be at rest at that point at that time. [This seems to be how Zeno at least
argued.]

Nevertheless, it seemed equally clear to others that moving bodies cannot be
depicted in this way, and that motion must be an 'intrinsic' (or even an
'inherent' property) of moving bodies (that is, we cannot depict moving bodies
in a way that would imply they are stationary), so that at all times a moving
body must be in motion, allowing it to be in and not in any given location at
one and the same time. [This seems to be Hegel's view of the matter -- but good
luck to anyone trying to find anything
that clear in anything
he wrote about this!]

If so, one or more of the above options must be rejected. To that end, it seems
that for the latter set of individuals 1) and 3) must be dropped, leaving only
2):

(2) Infinite divisibility is true of location only.

However, it's worth pointing out that the paradoxical conclusions classically
associated with these three alternatives only arise if other, less well
appreciated assumptions are either left out of the picture or are totally
ignored -- i.e., in addition to those alluded to above concerning the continuity
of space and the (assumed) discrete nature of time. As it turns out, the precise
form taken by several of these suppressed and unacknowledged premisses depends
on what view is taken of the allegedly 'real' meaning of the words like "motion"
and "place".

The above is taken from Essay Five at my site (where I detail several other
fatal objections to Engels and Hegel).

[Added on edit --
the above passage has been re-written extensively -- in order to make my argument
even clearer -- since
this comment was posted at the aforementioned site. Despite this, readers are
encouraged to visit
this site and see for themselves to what extent MLT is a
'stranger to the truth'.]

So, I
hope readers spotted my "This is silly, hah hah hah", and my "Yeah, I mean,
physics is kind of funny sometimes!" in there somewhere.

Furthermore, in the thread in question, I responded to FW's supposedly
'mathematical arguments' (which response MLT ignored); here is part of it.
First of all I quote Engels:

"As soon as we consider things in their motion, their change, their life, their
reciprocal influence…[t]hen we immediately become involved in contradictions.
Motion itself is a
contradiction; even simple mechanical change of place can only come about
through a body being both in one place and in another place at one and the same
moment of time, being in one and the same place and also not in it. And
the continual assertion and simultaneous solution of this contradiction is
precisely what motion is." [Engels (1976), p.152. Bold emphasis added.]

I did
this as part of my reply to the passage MLT quoted:

"When a body is
in motion its velocity is not zero and therefore...v = dx/dt =/= 0

"What we’re
discussing are fundamental facts of physics which you have to understand prior
to attempting to understand philosophical theories involving them....

"During motion, the position of a body in physical terms is defined by x and yet
it is not defined by x but is defined by dx. When in motion a body is at one
point x and yet it is at two points whose difference is dx. The same applies to
time -- you can define the body in motion at time t and yet there is a
difference of two times, dt, which also characterizes temporally a body in
motion. These are obviously contradictory conditions of motion, coexisting.
Motion is a constant resolution of these contradictions. This is what physics
says...."

I then
pointed out the following:

Here, he
[Engels] is quite clear: a body is "both in one place and in another place at
one and the same moment of time, being in one and the same place and also not in
it", that is, it moves with no time having lapsed.

If he had meant this:

E1: For some b, for two instants t(1) and t(2), b is at p at t(1) and not at p
at t(2), and b is at q at t(2).

where t(1) and t(2) both belong to some time interval T (such that dt =/= 0),
there would be no contradiction. His [Engels's] 'contradiction' depends on the
time difference between t(1) and t(2) being zero.

Which is why he [Engels] argued elsewhere as follows:

"How are these
forms of calculus used? In a given problem, for example, I have two variables, x
and y, neither of which can vary without the other also varying in a ratio
determined by the facts of the case.
I differentiate x and y,
i.e., I take x and y as so infinitely small that in comparison with any real
quantity, however small, they disappear, that nothing is left of x and y but
their reciprocal relation without any, so to speak, material basis, a
quantitative ratio in which there is no quantity. Therefore, dy/dx, the ratio
between the differentials of x and y, is dx equal to 0/0 but 0/0 taken as the
expression of y/x. I only mention in passing that this ratio between two
quantities which have disappeared, caught at the moment of their disappearance,
is a contradiction; however, it cannot disturb us any more than it has
disturbed the whole of mathematics for almost two hundred years. And now, what
have I done but negate x and y, though not in such a way that I need not bother
about them any more, not in the way that metaphysics negates, but in the way
that corresponds with the facts of the case? In place of x and y, therefore, I
have their negation, dx and dy, in the formulas or equations before me. I
continue then to operate with these formulas, treating dx and dy as quantities
which are real, though subject to certain exceptional laws, and at a certain
point I negate the negation, i.e., I integrate the differential formula, and in
place of dx and dy again get the real quantities x and y, and am then not where
I was at the beginning, but by using this method I have solved the problem on
which ordinary geometry and algebra might perhaps have broken their jaws in
vain." [Engels
(1976), p.175. Bold emphasis added.]

As he [Engels]
notes, it is the alleged "disappearance" of these 'quantities' (when they equal
zero, when dy/dx or dx/dt =0) that creates/constitutes the 'contradiction'.

And why he asserted:

"even simple
mechanical change of place can only come about through a body being both in one
place and in another place at one and the same moment of time,
being in one and the same
place and also not in it." [Bold added.]

According to
him, a moving body is in one place and not in it at the same time. In other
words it has moved while time
hasn't.

Much of
the rest of the discussion in the thread in question revolved around this point, and how
FW's interpretation of this part of DM differed from Engels's view of his own
theory, and of the Calculus. Now, there might be some readers who still agree
with FW (but, it isn't too clear how they could possibly do that if they want to defend Engels),
but how many who have read the above will think my words can be summarised as
follows: "This is silly, hah hah hah", or by "Yeah, I
mean, physics is kind of funny sometimes!"?

And yet,
MLT seems to be able to see words like this in there. Which suggests he either
didn't read my response to FW, or he prefers to tell lies -- or both.

I also go
on to point out (to FW) that his ideas are based on an obsolete 18th
century view of the calculus -- a point I don't expect MLT to be able to
grasp, since he, unlike me, hasn't got a degree in mathematics. Again, I add
this comment not to brag, or to 'pull rank', but merely to note that the only
reason MLT is impressed with FW's argument is that he knows rather too little
mathematics (and seems not to have read Engels too carefully, either!) -- as if dx/dt is a division!
[Which is how MLT depicts this symbol in the video.] It was a division
for 18th
century mathematicians, but no one since
Riemann
or
Weierstrass has argued this way (except perhaps the ignorant).

Moreover,
the points FW makes are mathematical, not physical. It isn't possible to
conduct an experiment (or imagine one that could be conducted -- even in an ideal
world, and the experimenter were possessed of 'god'-like powers of perception) to test and thus verify what he (or
Engels, or Hegel) had to say about motion; so it can't be Physics, can it?

In fact,
if anything is "'purely theoretical' and thus has 'no connection to reality'",
this argument of FW's is!

How come
MLT failed to spot this?

2)
Similarly, I defy MLT to find anywhere at the above Forum, or even at my site,
where I say anything that is remotely like this: "Oh, this is a contradiction,
therefore it's wrong".

It would be
very easy for me to 'refute' MLT by deliberately
making stuff up (and patently ridiculous stuff, too) about his ideas, wouldn't it? In
fact, in an earlier exchange, MLT pointed out that I had misrepresented him
(even though, unlike him, I didn't attribute to him a ridiculous or totally
fictitious set of beliefs),
so I apologised.

Will he do the same?

3) But,
what about this?

"The person
challenging them gives a completely sufficient refutation of their arguments to
which they don't respond with anything, and instead just, you know, just gloat
here to have demonstrated how this theory apparently leads to 'even more
ridiculous conclusions'."

Ok, so
let's go back to the original Essay where I supposedly said this -- only part of which was
quoted by MLT -- but this time, restoring the part he omitted:

One comrade has recently sought to challenge me on this; the
details can be found
here. In fact, I have shown that
Hegel and Engels's ideas about motion lead to even more ridiculous conclusions than this.
The reader is once again directed to Essay Five for more details --
here,
here, and
here.

Notice
the three occurrences of "here" at the very end? They are links to my site
where I reveal what these "even more ridiculous conclusions"
are; and, what is
more, I actually quoted one of these in full in the thread where I discussed
this with FW -- both of which MLT ignored, or preferred not to see.

Here
is one of them (this has again been taken from Essay Five, but slightly edited -- many of the points I
raise below depend on a detailed argument to be found in
the previous section of the Essay; I have also left the text the same size
as these remarks to save me having to re-size all those subscripts!):

The absurdity in L34b (below)
is quite plain for all to see and needn't detain us any
longer. However, the ludicrous nature of L17a
isn't
perhaps quite so obvious. It
may nevertheless be made more explicit by means of the following argument:

[L17a: Since a body can't be at rest and moving at
one and the same time in the same inertial frame, a moving body must both occupy
and not occupy a point at one and the same time.

L34b: Despite appearances to the contrary, all
bodies are at rest.]

(L35 below is an abbreviated version of Engels's theory.)

L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same instant.

L36: Let A be in
motion and at
(X1, Y1, Z1), at
t1.

L37: L35 implies that A is also at some other
point -- say,
(X2, Y2, Z2), at
t1.

L38: But, L35 also implies that A is at
(X2, Y2, Z2)and at another place at
t1;
hence it is also at (X3, Y3, Z3),
at t1,
otherwise it would be at rest at
(X2, Y2, Z2).

L39: Again, L35 further implies that A is at (X3, Y3, Z3)and at another place at
t1;
hence also at (X4, Y4, Z4), at
t1.,
otherwise it will be at rest at (X3, Y3, Z3).

L40: Once more, L35 implies that A is at (X4, Y4, Z4)and at another place at
t1;
hence also at (X5, Y5, Z5), at
t1....

By n successive applications of L35 it is
possible to show that, as a result of the 'contradictory' nature of motion, A
must be everywhere in its trajectory if it is anywhere, and all at t1!

But, that is even more absurd than L34b!

L34b: Despite appearances to the contrary, all bodies are
at rest.

The only way to avoid such an outlandish conclusion would be to maintain that L35
implies that a moving body is in no more than two places (i.e.,
less than three places) at once. But,
even this wouldn't help, for if a body is moving and in the second of those two
places, it can't then be in motion at this second location -- unless,
that is, it were
in a third place at the very same time (by L15 and L35). Once again,
just as soon as a body is located in any one place it is at rest
there, given this way of viewing things. The proposed dialectical derivation outlined above required
that
very assumption to get the argument going, repeated here:

L15: If
an object is located at a point it must be at rest at that point.

L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same instant.

Without L15 (and hence L35), Engels's conclusions wouldn't follow. So on this view, if a body is moving, it has to occupy
at least two points at once,
or it will be at rest. But, that is precisely what creates this latest
'problem': if that body is located at that second point, it must be at rest there,
unless it is also located at a third point at the same time.

This itself follows from L17 (now encapsulated in L17b):

L17: A moving body must both occupy and not occupy a
point at one and the same instant.

L17b: A moving object must occupy at least two
places at once.

Of course, it could be argued that L17b is in fact true of the
scenario depicted in L35-L40 -- the said body
does occupy at least two places at once namely
(X1, Y1, Z1) and (X2, Y2, Z2).
In that case, the above objection is misconceived.

Or, so it might be maintained.

[For those not too familiar with phrases like "at most two" or
"at least two"; if we remain in the
set of positive integers, the former means the same as "less than three"
(i.e., "two or less"), while the latter means the same as "two or more".]

The above objection would
indeed be misconceived if Engels had managed to show that a body can only be in
at most two (but not in at least two) places at once, which he not only failed to do,
he couldn't
do:

L17c: A moving object must occupy at most
two places at once.

That is because, between any two points there is a third point, and if the
body is in
(X1, Y1, Z1) and (X2, Y2, Z2),
at t1, then
it must also be in any point between
(X1, Y1, Z1) and (X2, Y2, Z2),
at t1--, say
(Xk, Yk, Zk).
But, as soon as that is admitted, there seems to be no way to avoid the
conclusion drawn above: if a moving body is anywhere, it is everywhere at the same time.

[And that is
why the question
was posed
earlier about
the precise distance between the points at/in which Engels says a body performs
such 'contradictory' marvels.]

Anyway, it would be unwise to argue that Engels believed this (or
even that DM requires it) -- that is, that a moving body occupies at most two points
at the same time -- since, as we have seen, if that body occupies the second of
these two points, it must be at rest at that point unless it also occupies a
third point at the same time. Given L15 (reproduced below), there seems no
way round this.

On the other hand, the combination here of an "at least two places at once"
with and an "at most two places at once" would amount to an "exactly two
places at once".

L17d: A moving object must occupy exactly two
places at once.

L15: If
an object is located at a point it must be at rest at that point.

However, any attempt made by DM-theorists to restrict a moving body to
the occupancy of exactly two places at once would once again only work if that body came to rest at the second of
those two points! L15 says quite clearly that if a body is located at a
point (even if this is the second of these two points), it must
be at rest at that point. In that case, the above escape route will only work
if DM-theorists reject their owncharacterisation of motion, which was
partially captured by L15. [This option also falls foul of the
intermediate points
objection, outlined earlier.]

In that case, if L15 still stands, then at the second of
these two proposed DM-points (say, (X2, Y2, Z2)),
a moving body must still be moving, and hence in and not in
that second point at the same instant, too.

It is worth
underling this conclusion: if a body is located at a second point (say, (X2, Y2, Z2)) at
t1,
it will be at rest there at t1, contrary to the assumption
that it is moving. Conversely, if it is still in motion at t1,
it must be elsewhere also at t1,
and so on. Otherwise, the condition that a moving body must be both in a certain place
and not in it at the very same instant will have to be abandoned. So,
DM-theorists can't afford to accept L17d.

Consequently, the unacceptable outcome --, which holds that as a result of the
'contradictory' nature of motion, a moving body must be everywhere along
its trajectory, if it
is anywhere, at the same instant -- still follows.

Again, it could be objected that when body A is in the second
place at the same instant, a new instant in time could begin. So, while
A
is in (X2, Y2, Z2)
at t1, a
new instant, say t2,
would start.

To be sure, this ad hoc amendment avoids the disastrous implications
recorded above. However, it only succeeds in doing so by introducing several
serious problems of its own -- for this
option would mean that
A
would be in (X2, Y2, Z2) at
t1
andt2,
which would plainly entail that A was located in the same place at two different times,
and that in turn would mean that it was stationary at that point!

It could be objected, once more, that A-like objects
occupy two places at once, namely
(X1, Y1, Z1) and (X2, Y2, Z2),
so the above argument is defective. Indeed, this is why the 'derivation' that
purports to show that a moving body must be everywhere along
its trajectory, if it is anywhere at the same instant can't work. We can perhaps clarify this objection by means of the following:

L38: L35 also implies that A is at
(X2, Y2, Z2)and at another place at
t1,
hence it is also at (X3, Y3, Z3)
at t1.

[L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same instant.]

The idea here is that if we select, pair-wise, any two
points that a body occupies in any order (either
(X1, Y1, Z1) and (X2, Y2, Z2),
or
(X1, Y1, Z1) and (X3, Y3, Z3)..., or
(X1, Y1, Z1) and (Xn, Yn, Zn),
and so on), then L17c will still be satisfied:

The 'DM-reply' proffered above held that Engels only needed a body to be in any two
places at once. But, the third place above -- (X3, Y3, Z3)
-- isn't implied by his description of the
'contradiction' involved. L38 (repeated below) only works by ignoring the fact that the
other place that in which A is located is precisely
(X1, Y1, Z1);
so, it can't be
in(X3, Y3, Z3) at that time --, or it doesn't have to be, which is all that is needed.So, when A is in (i)
(X1, Y1, Z1)
and (X2, Y2, Z2), and (ii)
(X1, Y1, Z1) and (X3, Y3, Z3),
and so on, it can't be in at most two places at once, since it is in this case in more than
two. The use of "and" scuppers this line-of-defence.

[It also
falls foul of an earlier response that if a moving object is in at most two
places at once, it must be stationary at the second of these locations.]

L38: L35 also implies that A is at
(X2, Y2, Z2)and at another place at
t1,
hence it is also at (X3, Y3, Z3)
at t1.

[L35: Motion implies that a body is in one place and not in it
at the same time; that it is in one place and in another at the same instant.]

It could be objected that the above response only works because
an "and" has been surreptitiously substituted for an "or". The original response in fact argued
as follows:

R1: If we select pair-wise any two
points a body occupies in any order (either
(X1, Y1, Z1) and (X2, Y2, Z2),or
(X1, Y1, Z1) and (X3, Y3, Z3)...,or
(X1, Y1, Z1) and (Xn, Yn, Zn),
and so on), then L17c will be satisfied.
[Underlining added.]

[L17c: A moving object must occupy at most
two places at once.]

But not:

R2: If we select pair-wise any two
points a body occupies in any order (i.e., (a)
(X1, Y1, Z1) and (X2, Y2, Z2),and(b)
(X1, Y1, Z1) and (X3, Y3, Z3)...,and (c) ((X1, Y1, Z1) and (Xn, Yn, Zn),
and... (d)...,
and so on), then L17c will be satisfied.

Unfortunately, once more, this reply simply catapults us back to an
earlier untenable position, criticised above, as follows:

That is because, between any two points there is a third point, and if the
body is in
(X1, Y1, Z1) and (X2, Y2, Z2),
at t1, then
it must also be in any point between
(X1, Y1, Z1) and (X2, Y2, Z2),
at t1--, say
(Xk, Yk, Zk).
But, as soon as that is admitted, there seems to be no way to avoid the conclusion drawn
above: that if the body is anywhere, it is everywhere at the same time.

In that case, the reply encapsulated in L38/R1 fails, too. So, if a
body is in
(X1, Y1, Z1)
and (X2, Y2, Z2)
at t1, it
must also be in at least one of the intermediate points -- say,
(Xk, Yk, Zk)
--
also at t1.
Hence, R2 is still a valid objection.

In order to see this, a few of the subscripts in R2 need only be
altered, as follows:

R3: If we select pair-wise any two
points a body occupies in any order (i.e., (a)
(X1, Y1, Z1) and (X2, Y2, Z2),and(b)
(X1, Y1, Z1) and (Xk, Yk, Zk)...,and (c)
(X1, Y1, Z1) and (Xi, Yi, Zi)...,
and so on), then L17c won't be satisfied.

It is surely philosophically and mathematically irrelevant whether we label
points with iterative letters (i.e., "k" or "i") or with
numerals ("1", "2", or "3"). [Recall, the variables labelled with iterative letters
(i.e., "k" or "i") are intermediate points.]

In which case, R3 implies that if a body is in, say,
(X1, Y1, Z1)
and (X2, Y2, Z2),
at t1, it
must also be in at least one of the intermediate points, say,
(Xk, Yk, Zk),
at the same moment. R3 thus implies
that L17c is false.

Moreover, it is also worth asking
the following
in relation to L38: Is A at
(X2, Y2, Z2), at t1?
If it is, then it must be elsewhere at the same time, or it will be stationary,
once more.
So much is agreed upon. In that case, the only way to stop the absurd induction
(i.e., the one that derived the conclusion that if a moving body is anywhere it
must be everywhere at the same time) would be to
argue as follows:

L38a: L35 also implies that A is at
(X2, Y2, Z2)and at another place at
t1,
hence it is also at (X1, Y1, Z1),
at t1,
but not at (X3, Y3, Z3),
at
t1.

[L38: L35 also implies that A is at
(X2, Y2, Z2)and at another place at
t1,
hence it is also at (X3, Y3, Z3),
at t1.

L35: Motion implies that a body is in one place
and not in it at the same time; that it is in one place and in another at the
same instant.]

However, this 'straw', once clutched, has unfortunate
consequences that desperate dialecticians might want to think about before they
claw at it too frantically:

L38b: If A is at
(X2, Y2, Z2)
and (X1, Y1, Z1),
at t1,but not at (X3, Y3, Z3),
at t1,
then it must be at (X3, Y3, Z3), at
t2.

L38c: If so, A will be at two places --
(X2, Y2, Z2) and (X3, Y3, Z3)
-- at different times (i.e.,
(X2, Y2, Z2),
at t1,
and (X3, Y3, Z3),
at t2).

L38d: In that case, between these two locations
(i.e., (X2, Y2, Z2)
and (X3, Y3, Z3)), the motion
of A will cease to be contradictory -- since it will not now be in
these two places at the same time, but at different times.

So, it seems that dialecticians can
only escape from the absurd consequence of their theory -- that a moving object
is everywhere at the same time -- by abandoning their belief in the
contradictory nature of motion at an indefinite number of intermediate locations
in its transit -- for example, right after it leaves the first two places it
occupied in that journey!

Now, if the conclusions above are valid
(that is, if dialectical objects are anywhere in their trajectories, they are
everywhere all at
once), then it follows that no moving body can be said to be anywhere
before it is anywhere else in its entire journey! That is because such
bodies are everywhere all at once. If so, they can't be anywhere first and then
later somewhere else.

In the dialectical universe, therefore, when it come to motion
and change, there is no before and
no after!

In that case, according to this 'scientific theory', concerning
the entire trajectory of a body's motion, it would not only be impossible to say it was at the beginning of its journey
before
it was at the end, it would be incorrect to say that! In fact, it would be at the end of its journey at the same
time as it sets off! So, while you might foolishly think, for example, that you
have to board an aeroplane (in order to go on your holidays) before you disembark at your
destination, this 'path-breaking' theory tells us you are sadly mistaken: you
not only must get on the plane at the very same time as you get off it at the 'end',
you do!

Whether
or not the reader agrees with the above arguments, one thing I hope is clear: I
do not "gloat" over anything; I attempt to substantiate what I allege with
detailed argument. Would that DM-supporters did the same!

"The rest of their
counter-arguments are just silly. Instead of contesting the fact that things in
motion exist in multiple places at the same time, they turn around and argue
that really all physical bodies exist in multiple places, for example, beans
exist inside a tin and inside a store. or your head and your feet exist in
different places despite being your body. However, this is simply word-play. The
point they're making is that things don't exist in a single point but in an
area, but that has no impact on the argument whatsoever on Engels nor anyone
that the Trotskyite is arguing against has (sic) ever claimed that humans, beans
or tin cans exist in a single point. It's obvious that wasn't what Engels was
arguing about. Besides, this kind of talk is metaphysical. And then they proceed
to say that 'You know, this is an...um.., mistake by Engels because this kind of
idea applies to things that are not in motion, for example, you know..., beans
in tin cans'. But as I just pointed out, that's not what Engels was talking
about at all because, yeah..., well, you get the point. It's just, er..., word
games to say 'Oh, beans exist inside a tin can inside a warehouse...,' that's..
obviously it's not the same location, it's not the same point existing inside a
tin and also inside a factory or a warehouse, whatever, doesn't mean they exist
in two different points."

It is
reasonably clear from this that MLT has missed the point. Here it is again:

Finally, as noted above, this 'contradiction' is a direct consequence of the
glaring ambiguities built into Zeno's (and thus Hegel and Engels's) account of motion
-- that is, in their use of certain words
(like "moment", "move", and "place"). This means that when these
equivocations have been resolved, the 'contradictions' simply disappear.
[Once again, that disambiguation
has been carried out
here.]

"It's just, er...,
word games to say 'Oh, beans exist inside a tin can inside a warehouse...,
that's.. obviously it's not the same location, it's not the same point existing
inside a tin and also inside a factory or a warehouse, whatever, doesn't mean
they exist in two different points."

Does
MLT mean by "point" (and/or "location") a mathematical point? Or does he
intend some other meaning? If he means a mathematical point, then
he can't be referring to physical objects (of the sort that Engels was
referring to -- i.e., those that exist in the "real world" (to use MLT's own
phrase, here). Gross bodies in the "real world" do not occupy "a point" (or even an
"area" (as MLT also says(!) -- unless they have been flattened into a two-dimensional
manifold), but a volume interval, or sub-space of 3-space.

And it is
little use telling us what Engels meant, since he was equally unclear; and that is
why I raised the issues I did. Of course, they were deliberately simplified, since the
Essay MLT was criticising was aimed "at novices"!

However,
in Essay Five, I enter into this very topic in considerable detail; here is just
a brief excerpt (slightly edited):

Engels tells us that a body must be:

"[B]oth in one place and in another
place at one and the same moment of time, being in one and the same place and
also not in it." [Engels (1976),p.152.]

Here, he appears to be claiming two separate things that
do not immediately look equivalent:

L1: Motion involves a body being in one place and in
another place at the same time.

L2: Motion involves a body being in one and the
same place and not in it.

L1 asserts that a moving body must be in
two places at once, whereas L2 says that it must both be in one place
and not in it, while leaving it unresolved whether it is in a second place
at the same or some later time -- or even whether it could be in morethan two places at once. To be sure, it could be argued that it is implicit in
what Engels said that these events occur in the "same moment of time"; however, I am
trying to cover every conceivable possibility, and it is certainly
possible that he not only did not say this, he didn't even intend it. [The significance of these comments will emerge as the Essay
unfolds.]

It is also far from easy to see how a moving body can be "in one
place and not in it", and yet still be in two places at once.
If moving object Misn't located at X -- that is, if
it is not in X
--, then it can't also be located at X (contrary to what Engels
asserts). On the other hand, if Mis located at X, then it can't also not be at X!
Otherwise, Engels's can't mean by "not" what the rest of us mean by that word.
But, what did he mean?

At this point, we might be reminded that there is
a special sort of 'dialectical' "not" [henceforth "notD"]
which can also mean, it seems, "Maybe this isn't a 'not' after all; indeed,
it's the exact opposite of 'not'". And yet, if
the meaning of "not" is so malleable, how can we be sure we know what "motion"
and "place" mean, let alone "dialectical". If "notD"
can mean the opposite of the everyday, ordinary "not", then perhaps "motion" can
also mean "stationary", and "dialectical" can mean "metaphysical" (in the sense
of this word as it
was used by Hegel and Engels).

But, when a DM-theorists tells us that "notD"
does not
mean "not", what are we to say of the "not" in the middle (the one coloured
red)? If "not" can slide about effortlessly in this manner, then perhaps this
red "not" might do likewise, and mean its opposite, too? If so, when a DM-theorist
tells us that "notD"
does not
mean "not", who can say whether or not he/she actually means the following:
"'NotD'
does not not (sic) mean 'not'" -- which pans out as "'NotD'
means 'not'"; at which point the 'dialectical "not" collapses back into an
ordinary "not". A rather fitting 'dialectical inversion' if ever there was one.

Until DM-theorists come up with
non-question-begging criteria that inform us unambiguously which words don't
'dialectically' develop into their opposites and which do, the above
'reminder' can be filed away in that rather large box labelled "Dialectical Special Pleading".

[Anyone who objects to the above argument
hasn't read the DM-classics,
where we are told that everything in the universe -- and that must include
words, which, it seems, do exist in this universe -- struggles with and
then turns into its opposite.]

On the other hand, if this theory can only be
made to work by fiddling with the meaning of certain words, how is that
different from imposing this theory on the facts,
something that Engels, at
least, disavowed?

Be this as it may, if M is in two places at once --
say in X and Y at the same time --, then it can't just be in Y
but must be in Yand another place -- otherwise it will
be stationary at Y!

Returning to the main feature: it is
important to be clear what Engels meant here because L1 is actually
compatible with the relevant body being at rest! This can be seen if we
consider a clear example: where an extended body is motionless
relative to an
inertial frame.
Such a body could be at rest and in at least
two places at once. Indeed, unless that body were itself a mathematical
point, or maybe discontinuous in some way, it would occupy the entire space
between at least two distinct spatial locations (i.e., it would occupy a finite volume interval
-- or more colloquially, it would take up some space). But since all real,
materialbodies are
extended in this way, the mathematical point option seems irrelevant, here.
[Anyway, it, too, will be considered again, below.]

[Added on edit: the above comments (as well as those below)
should be of interest to MLT since he seems to prefer it if we concentrate on
objects and processes that have a genuine "connection to reality", and which
aren't "purely theoretical" -- and real material bodies take up space.
Only mathematical points do not do this.]

A commonplace example of this sort of situation would be where, say, a train is at rest relative to a platform.
Here, the train would be in countless places at once, but still stationary
with respect to some inertial frame. [There are innumerable examples of this
everyday phenomenon, as I am sure the reader is aware.]

[In this and
subsequent paragraphs I will endeavour to illustrate the alleged ambiguities in
Engels's account by an appeal to everyday situations (for obvious materialist
reasons). However, these can all be translated into a more rigorous form using
vector algebra and/or set theory. In the last case considered below, just such a
translation will be given to substantiate that particular claim. (That has been
done here.)]

Unfortunately, even this ambiguous case could involve a further equivocation
regarding the meaning of the word "place" -- the import of which Engels clearly
took for granted. As seems plain, "place" could either mean the general location
of a body (roughly identical with that body's own topological shape, equal in
volume to that body --, or, on some interpretations of this word, very slightly
larger than its volume so that the body in question can fit 'inside' its
containing volume interval). Alternatively, it could involve the
use of a system of precise spatial coordinates (which would, naturally, achieve something
similar), perhaps pinpointing its centre of
mass and using that to locate the body, etc.

Of course, as noted above, Engels might have been referring to the motion
of mathematical points, or point masses. But, even if he were, it
would still leave unresolved the question of the allegedly contradictory nature
of the motion of gross material bodies, and how the former relate to the
latter.

It is Engels's depiction of motion that is unclear; because of
that, I
will concentrate on ordinary material bodies. Anyway, since DM-theorists hold that their theory can account for motion in the real world, the
motion of mathematical points -- even where literal
sense can be made of such 'abstract points, or, indeed, of the idea that they canmove
(after all, if such points do not exist in physical space, they can hardly be said to move)
-- won't in
general be entered into here.

Moving on to
L2 (no pun intended): this sentence also involves further ambiguities that similarly fail to
distinguish moving from motionless bodies. Thus, a body could be located within an extended region
of space and yet not be totally inside it. In that sense, it would be both in and
not in that place at once, and it could still be motionless with respect
to some inertial frame.

Here, the
equivocation would centre on the word "in". To be sure, it could be
objected that "in" has been illegitimately replaced by "(not) totally or wholly
inside/in". Even so, it is worth noting that Engels's actual words imply that
this is a legitimate, possible interpretation of what he said:

L2: Motion involves a body being in one and the
same place and not in it.

If a body is "in and not in" a certain place it
can't be
totally in that place, on one interpretation of these words. So, Engels's
own words allow for his "in" to mean "not wholly in".

A mundane example of this might be where, say, a 15 cm long
pencil is sitting in a pocket that is only 10 cm deep. In that case, it would be
perfectly natural to say that this pencil is in, but not entirely
in, the pocket -- that is, it would be both "in and not in" the pocket at the same
time (thus fulfilling Engels's definition) --, but still at rest with respect to some inertial frame.
L2 certainly allows for such a situation, and Engels's use of the word "in" and
the rest of what he said plainly carry this interpretation.

Hence, it
seems that Engels's words are compatible with a body being motionless
relative to some inertial frame.

This is still the case even if L1
and L2 are combined, as Engels intended they should:

L3: Motion involves a body being in one place and
in another place at the same time, and being in one and the same place and not
in it.

An example of L3-type
--
but apparently
contradictory -- 'lack of motion' would involve a situation where, say, a car is
parked half in, half out of a garage. Here the car is in one and the same place
and not in it ("in and not in" the garage), and it is in two places at once (in the garage
and in the grounds of a house),
even while it is at rest relative to a suitable inertial frame.

In which
case, the alleged contradiction that interested Engels can't be the result ofmotion (since his own words are compatible with a body being at rest -- that
is, what he alleged isn't unique to moving bodies); it is in fact a consequence of the vagueness or the ambiguity of his description.

Objects at rest relative to some inertial
frame can and do display the same apparent 'contradictions' as
those that are in motion with respect to the same inertial frame. Naturally, if things
at rest share the very same vague or ambiguous features (when they are expressed in language) as those
that are in motion, Engels's description clearly fails
to pick out what is unique to
moving bodies.

This isn't a good start. We still lack a
clear and unambiguous DM-description of motion!

At
best,
L3 depicts the necessary,
but not the sufficient conditions for motion. [But, as we will see later, not
even this is true.] In that case, the alleged
contradictory nature of L3 has nothing to do with any
movement
actually occurring, since the same description could be true of bodies at rest,
which share the same necessary conditions. As already noted, alleged paradoxes
like this arise from the ambiguities implicit in the language Engels himself
used -- and, as it turns out, in language he misused. [This will also be discussed in greater
detail below (that is, "below" in Essay Five; this material hasn't been
reproduced here).]

Nevertheless, in the next few sections several attempts will be
made to remove and/or resolve these
equivocations in order to ascertain what, if anything, Engels might have
meant by the things he tried to say about moving bodies. Alas, all of them fail....

In which
case, it
isn't at all clear what Engels meant by the terms he used, and to drive this
point home, I added these comments (to Essay Five):

Many of the ambiguities mentioned above (in relation to Engels's analysis of
"motion") actually depend on systematic vagueness in the meaning of the word
"place" and its cognates. Even when translated into the precise language of
coordinate algebra/geometry, the meaning of this particular word doesn't become much clearer
(when used in such contexts).

Of course, this isn't to criticise the vernacular;
imprecision is one of its strengths. Nor is it to malign mathematics! However,
when ordinary words are imported into Philosophy, where it is almost invariably
assumed they have a single unique (or 'essential') meaning, problems invariably
arise....

Indeed, as it turns out, there is no such thing as
the meaning of the word "place" -- or, for that matter, of "move".

This lack of clarity carries over into our use of technical terms
associated with either word; the application of coordinate systems, for example,
requires the use of rules, none of which is self-interpreting. [The point of
that comment will emerge presently.]

Nevertheless, it is relatively easy to show (by means of the sort of selective
linguistic 'adjustment' beloved of metaphysicians, but applied in areas and
contexts they generally fail to consider, or, rather, choose to ignore)
that ordinary objects and people are quite capable of doing the
metaphysicallyimpossible. The flexibility built into everyday language actually 'enables'
the mundane to do the magical, and on an alarmingly regular basis. Such
everyday 'prodigies'
do not normally bother us -- well, not until some bright spark tries to do a little
'philosophising' with them.

[Added on edit: it needs underlining that I am being
ironic here!]

If the
ordinary word "place" is now employed in one or more of its usual senses, it is
easy to show that much of what Engels had to say about motion becomes
either false or uninteresting. Otherwise, we should be forced to concede
that ordinary people and objects can behave in extraordinary -- if not
miraculous --
ways.

Consider,
therefore, the
following example:

L41: The strikers refused to leave their place of
work and busied themselves building another barricade.

Assuming that the reference of
"place" is
clear from the context (that it is, say, a factory), L41 depicts objects
moving while they remain in the same place -- contrary to what
Engels said (or implied) was possible. Indeed, if this sort of motion is
interpreted metaphysically, it would involve ordinary workers doing the
impossible -- moving while staying still!

Of course, an obvious objection to the above would be that L41 is a highly contentious example,
and not at all the sort of thing that Engels (or
other metaphysicians) had in mind by their use of the word "place".

But, Engels didn't
tell us what he meant by this term; he simply assumed we'd understand his
use of it. If, however, it is now claimed that he didn't mean by "place"
a sort of vague "general location" (like the factory used in the above example), then that would confirm the point being made in this part of the
Essay: Engels didn't say what he
meant by "place" since there was nothing he could have said
that wouldn't also have ruined his entire argument. Tinker around with the word
"place" and the meaning of "motion" can't fail to be compromised
(as noted above). This can
be seen by considering the following highly informal 'argument':

L42: Nothing that moves
can stay in the same place.

L43: If anything stays in the same place, it
can't move.

L44: A factory is one place in which workers
work.

L45: Workers move about
in factories.

L46: Any worker who moves can't stay in the same place
(by L42, contraposed).

L47: Hence, if workers move they can't do so in
factories (by L44 and L45).

L48: But, some workers stay in factories while
they work; hence, while there they can't move (by L43).

L49: Therefore, workers work and do not work in factories, or
they move and they do not move.

As soon as one meaning of
"place" is
altered (as it is in L44), one connotation of "move" is automatically affected
(in L45), and vice versa (in both L47 and L48). In one sense of
"place", things can't move (in another sense of "move") while staying in one
place (in yet another sense of "place"). But, in another sense of both they
can,
and what is more, they can typically do both. Failure to notice this produces 'contradictions'
to order, everywhere (as in L49).

Even so, who believes that workers work and do not
work in factories? Or, that they move and do not move while staying in the same place?

Perhaps only those who "understand" dialectics...?

Clearly, Engels's 'theory' of motion has to be able to take account of ordinary objects if it
is to apply to the real world and not just to abstractions, or to
physically meaningless mathematical 'points'. But, this is precisely what his
'theory' can't do, as we
are about to
see.

It could be
objected that it would be possible to understand what
Engels and Hegel were trying to say if "place" is defined precisely
without altering the meaning of "move", contrary to the points raised in the
last few sections of this Essay. In that case, it could be argued that if "place"
is defined by the use of precise spatial coordinates (henceforth, SCs), Engels's
account of motion would become viable again.

Or, so some might like to think.

Of course, the problem here is that in the example
above (concerning those
contradictory mobile/stationary workers), if we try to refine the meaning of the
word "place" a little more precisely, it will come to mean something like "finite (but
imprecise) three-dimensional region of space large enough to contain the
required object". Well, plainly, in that sense things can and do move
about while they remain in the same region (i.e., "place") --
since, by default, any object occupies such a region as it moves -- that
is, it must always occupy a three-dimensional region of space large enough
to contain it as it moves; it certainly doesn't occupy a larger or a smaller space
(unless it expands/contracts)! Moreover, objects occupy finite
regions as they move in relation to each other (or they wouldn't be able to move).

Hence, if defined this way, moving objects always occupy the same space, and
hence they don't move! That is, if they always stay in the same space, they
can't move -- if we insist on defining motion the way Engels and Hegel
thought they could.

As we have seen, objects always occupy the same space, even as they
move. So, they both move and don't move! Plainly we need to be more precise.

Of the many problematic options there are before us, the following seem
to be most relevant to the
points at hand:

(1) If an object always occupies the same space
(which fits it like a glove, as it moves), then it can't actually move!

(2) If it occupies a larger space as it moves, it must expand.

(3) If it moves about in the same region of
space (such as a factory), it still can't move!

(4) If it
successively occupies spaces equal to its own volume as it moves, the
situation is even worse, as we will soon
see.

Hence, if the
'regions' mentioned above are constrained too much, nothing would be able to move
-- this is Option (1).
Put
each worker in a tightly-fitting steel box that exactly fits him or her and
watch all locomotion grind to a halt.

On the other hand, put that worker in a larger region of space, and he/she
still won't be
able to move
-- this is Option (3). That is because if we define motion as successive occupancy of
regions of space within a broader region, then this worker can't move since he/she is always in the same
broader region, the same space.

The difficulty here is plainly one of
relaxing the required region (that an object is allowed to occupy) sufficiently enough to
enable it to move from
one place to another without stopping it moving altogether -- that is,
preventing Option (3) from undermining Option (4) --, all the while
providing an account that accommodates the movement of medium-sized objects in
the real world. But, once this has been done the above difficulties soon
re-appear, for it is quite clear that objects still move while staying in the
same place -- if the place allowed for this is big enough for them to do just
that!

Indeed, this fact probably accounts for, or permits, most (if not all) of the
locomotion in the entire universe. Clearly, in the limit, if anything moves in nature it must remain in the
same
place, i.e., it must remain in the universe! Unless an object travels beyond the
confines of the universe, this must always be the case: the said object moves while remaining in the same
place -- i.e., the universe! Of course, this relaxes the definition
of "same place" far too much. But, the problem now is how to tighten the definition
of "place" so that objects aren't put in straight-jackets once more. [I.e., Option (1).]

At first sight, the above objection (concerning a
precise enough definition of
"place") seems reasonable enough. Engels clearly meant something a little more
precise than a vague or general sort of location (like a factory). But, if so, what?
He didn't say, and his epigones haven't, either -- indeed, it is quite clear
that they
don't even recognise this as a problem, so sloppy has their thought become.
[Good luck finding a clear definition in Hegel!]

It might seem possible to rescue Engels's argument if tighter protocols for
"place" are prescribed --, perhaps those involving a reference to "a (zero
volume) mathematicalpoint, in three-dimensional space, located by the use of precise
SCs". But, this option would embroil Engels's account in far more intractable
problems. That is because such an account would (plainly!) relate to
mathematical point locations, or the movement of mathematical points
themselves -- and we saw earlier that that was a non-starter.

[SC = Spatial Co-ordinate.]

Clearly, things cannot
move about in such points -- but this has nothing to do with the supposed nature of reality.
These 'entities' do not (and could not) exist in nature for them
to contain anything. That is because mathematical points aren't containers.
They have no volume and are made of nothing. If this weren't the case, they
wouldn't be mathematical points, they'd be regions.

As noted above, if Engels meant something like this by his use of "place", his
account would fail to explain or accommodate the movement of gross material
bodies in nature, for the latter do not
occupy mathematical points.

And, it is no use appealing to larger numbers/sets of such points located by SCs
(or other technical devices);
no material body can occupy an arbitrary number of points, since points
aren't
containers.

Perhaps we could define a region (or a finite volume
interval) by the use of SCs? Maybe so, but this would merely introduce another
classical conundrum (which is itself a variation on several of
Zeno's
other paradoxes): how it is possible for a region (or a volume interval) to be composed of
points that have no volume. Even an infinite number of zero volume
mathematical points adds up to zero. Now, there are those who think this
conundrum has a solution (just as there are those who think it doesn't), but it
would seem reasonably clear that the difficulties surrounding Engels's 'theory'
aren't likely to be helped by importing several more of the same from another set of
paradoxes -- especially when these other paradoxes gain purchase from the same
linguistic ambiguities and vagaries about "space", etc.

Be this as it may, it is far more likely that Engels's use of the word "place"
is an
implicit reference to
a finitethree-dimensional volumeinterval (whose limits
could be defined by the use of well-understood rules in
Real
and
Complex Analysis,
Vector
Calculus, Coordinate Algebra and
Differential Geometry,
etc.).

Clearly, such volume intervals must be large enough to hold (even temporarily) a
given
material object. If so, this use of the phrase "volume interval" would in principle
be no different from the earlier use of "place" to depict the movement of those workers!
If
they can move about in
locations big enough to contain them, and who remain in the same place while doing so,
Engels's moving objects can do so, too -- except they would now have a more precise "place"/region
in which to do it.

However, and alas, this sense of "place" is no use at all, for
when such workers move, they will, by definition, stay in the same place! So, it
seems must be the case with Engels's moving objects, if we depict "place" this
way. [This
is just Option
(3), again!]

Naturally, the only way to avoid this latest difficulty would be to argue that the location
of any object must be a region of space (i.e., volume interval) equal
to that object's
own volume.
This is in effect
one
of the classical definitions. In that case, as the said object moves, its
own exact volume interval would move with it, too; the latter would follow each moving object around more
faithfully than its own shadow, and more doggedly than a world-champion bloodhound. But,
plainly, if that were the case, it would mean that such objects would still move while
staying in the same place -- since, plainly, any object always occupies a
space equal to its own volume, which would, on this view, travel everywhere with it, like a sort
of metaphysical glove. [Option (1),
again!]

As should now seem plain: in this case we now have two problems where once
there was just one, for we should now have to explain
not only how bodies move, but how it is also possible for volume intervals to move so that they can
faithfully shadow the objects
they contain!

Moreover, and far worse: in this instance, not only would we have to explain how locations
(i.e., volume intervals) are themselves capable of moving, we would also
have to explain what on earth they could possibly move into!

What
sort of
ghostly regions of space could we appeal to, to allow regions of space
themselves to move into them?

Even worse still: these 'moving volume intervals'
must also occupy volumes equal to their own
volume, if they are to move (given this 'tighter' way of characterising
motion). And, if they do
that, then these new 'extra' locations containing the volume intervals themselves must
now act
as secondary
'metaphysical containers', as it were, to the original 'ontological gloves' we
met earlier. Metaphorically speaking, this
theory, if it took such a turn, would be moving backwards, since an
infinite regress would soon confront us, as spatial mittens inside containing
gloves, inside holding gauntlets, piled
up alarmingly to account for each successive spatial container, and how each of
them could
possibly move. As seems reasonably clear, we would only
be able to account for locomotion this way if each moving object were situated
at the centre of some sort of 'metaphysical onion', each with a potentially infinite
number of 'skins'! [IteratedOption (1)!]

It could be countered that even though objects occupy spaces equal
to their own volumes, as they move along they then proceed to occupy successive
spaces of this sort (located in the surrounding region, for example), all of
which are of precisely the right volume to contain the moving object that now
occupies them, and which can be located/defined precisely. On this revised
scenario, moving objects would leave their old locations (their old
containers) behind as they barrelled along.

This now brings us to a consideration of Option (2), and/or Option (4) -- now
modified to (4a) --, from earlier:

(2) If an object occupies a larger space as it moves, it must
expand.

(4a) An object
successively occupies spaces (or volume intervals) equal to its own volume as
it moves.

I will reject (2) as absurd. If anyone wants to defend it,
they are welcome to all the headaches it will bring in its train.

Considering, now, Option (4a):

Even if (4a) were a correct interpretation of what Engels meant,
and it were also a viable option
-- and, indeed, if sense could be made of these new, and accommodating
successive locations without re-duplicating
the very same problem noted in the previous few paragraphs --, no
DM-theorist could afford to adopt it. That is because dialecticians claim that moving
bodies occupy at least two such "places" at the same time,
being in one
of them and not in it at the same moment. Clearly, if motion were defined in such
terms (that is, if it were characterised as involving objects successively occupying spaces
equal to their own volumes), then moving objects would occupy at least two of
these
volume intervals at once.

In that case, 'dialectical objects' would not so much move as stretch or
expand! [Modified Option (2)!]

To see this point more clearly (no pun intended!), it might be useful to examine the above
argument a little more
closely.

If the centre of mass (COM) of a 'dialectically moving' object, D, were located at, say,
(Xk, Yk, Zk)
and (Xk+1, Yk+1, Zk+1), at the same time (to satisfy the requirement that moving bodies occupy at least two such "places" at the same time,
being in one of them and not in it), it would have to occupy a space larger than its own volume
while doing so.

Let us call
such a space "S", and let the volume interval containing
(Xk, Yk, Zk)
and (Xk+1, Yk+1, Zk+1) be
"δV1",leaving it open for the time being
whether S and δV1 are the
same or are different. Thus, if the COM of D is in two
such places (i.e.,
(Xk, Yk, Zk)
and (Xk+1, Yk+1, Zk+1))at once,
D would plainly be in S, and would occupy δV1. But, once again, that would
mean that D would move while remaining in the same place -- i.e., it
would remain inside S, or inside δV1 (whichever is preferred), as its COM moved from
(Xk, Yk, Zk)
to (Xk+1, Yk+1, Zk+1),
in the same instant. [Option (3), again!]

[Except, we can't speak of a 'dialectal object' moving from
one point to the next since that would imply it was in the first
before it was in the second, and that it was in the second after it
was in the first. As we have seen, if such an object isin both
places at the same time, there can be no "before" and no "after",
either.]

Now, the only way to avoid the conclusion that D moves
while occupying the same place/space S and/or δV1
--, and hence that it appears to stay still while it moves, just like the 'mobile/stationary' workers we encountered earlier --
would be to argue that
such spaces remain where they are while Dmoves into successively new
locations, or new spaces. This seems to be the import of
Option (4a):

(4a) An object
successively occupies spaces (or volume intervals) equal to its own volume as
it moves.

But, as D moves it still occupies δV1,
only we would now have to argue that as it does so it also moves into a newδV
each time, say, δV2
-- except that δV2 must
now contain (Xk+1, Yk+1, Zk+1) and (Xk+2, Yk+2, Zk+2)
-- otherwise it wouldn't be a new
containing volume interval that satisfied the requirement
that moving bodies occupy at least two such "places" at the same time,
being in one of them and not in it.

Plainly, all objects have to occupy some volume interval or other
at all times (or they would 'disappear'). However, in D's case it has to do this
while also occupying new volume intervals at the same time as it moves
along (otherwise, as we saw, it would move while being in the same place, which
would imply that it didn't move, after all!).

So, if D
occupies only one S or only one
δV at once, it would be at rest in either. [Options (1)
and (3).] Hence, it must occupy at least two
of these at the same time (if, that is, we accept the 'dialectical' view of motion).

If so, the only apparent way of avoiding the conclusion that D-like
objects move while staying still is to argue that they occupy two successive
Ss, or two successive δVs (perhaps these partially 'overlap',
perhaps they don't), at once. Unfortunately, this would now mean that D-like
objects would have to occupy a volume/volume interval bigger than either of S
or δV at once, and hence: they must expand or stretch.

It could be objected that two successive δVs would
contain
(Xk, Yk, Zk)
and
(Xk+1, Yk+1, Zk+1)
each between them
--
that is, δV1
would contain
(Xk, Yk, Zk)
and δV2
would contain (Xk+1, Yk+1, Zk+1)
--, so the above objection is misguided. Maybe so, but the point is that dialectical
objects must occupy two δVs
at once, and if that is so, both δVs must
contain
(Xk, Yk, Zk)
and (Xk+1, Yk+1, Zk+1),
jointly or severally, otherwise such moving objects couldn't occupy two spaces (two δVs) at
the same time.

But, if that is so, and D isn't stationary while it
occupies δV2
--
and as we saw above in an analogous context
-- it must also occupy δV3at the same time, and so on.
Successive applications of this
argument would have D occupying bigger and bigger volume intervals (i.e., δV1 + δV2 + δV3 + δV4 +...,+ δVn),
all at the same time. In
the limit, D could fill the entire universe (or, at least, the entire
volume interval encompassing its own trajectory), all at the same time -- if it moves, and
if Hegel is to be believed!

There thus seems to be no way to depict the
motion of D-like objects that prevents them from either (i) moving while staying
still, or, from (ii) expanding alarmingly like some sort of metaphysical
Puffer Fish....

The reader should now be able to see for
herself what mystical mayhem is introduced into our reasoning by this cavalier
use of (contradictory) metaphysical language. When one sense of "move" is
altered, one sense of "place" can't remain the same, nor vice versa.

Of course, no one believes the above
ridiculous conclusions, but there appears to be no way to avoid them using the
radically defective and hopelessly meagre conceptual and/or logical resources DL supplies its
unfortunate victims....

Despite this,
it could be argued that if the ordinary word "place" is so vague then it should
be replaced by more precise concepts; those defined in terms of SCs,
once more. But, as the following argument shows, that would be another backward
move (no pun intended!):

[R3 is just a
mathematical shorthand for three-dimensional
Cartesian Space.]

L52: However, when written correctly, the elements in such
3-tuples
must occupy their assigned places (by the ordering rules). Consider then the
following ordered triplet: <x1, y1,
z1>.
Each element in such an SC must be written precisely this way, with xi,
yi, and
zi
(etc.) all in their correct places.

L53: But, the situating of such elements can't itself be
defined by exact SCs, otherwise an infinite regress will ensue.

L54: Consequently, this latter sense of "place"
(i.e., that which underlies the ordering rules for SCs) can't be defined (without circularity)
by means of SCs.

[SC = Spatial Coordinate.]

This means that the definition of "place" by means of SCs is itself
dependent on a perfectly ordinary meaning of "place", and, further,
that the latter sense of "place" must already be understood if a co-ordinate system is
to be set-up correctly.

Therefore, the ordinary word "place" can't be defined without circularity by means of a coordinate
system.

In short, the precision introduced by means of SCs is bought at the expense of
presupposing mundane linguistic facts such as these.

Of course, this isn't to malign or depreciate coordinate geometry, it merely
serves to
remind us that any branch of human knowledge (even one as technical and
precise as modern
mathematics) has to mesh with ordinary language and everyday practice (at
some point), if it is to be set-up to begin with, and if human beings (or
machines programmed by human beings) are to use it. Everyday facts like these are
soon forgotten (in the course of one's education), since, as
Wittgenstein
pointed out, we are taught to quash or dismiss such simple questions very early
on. As a result we inherit the mythological structures that previous generations
have built on top of unexamined foundations like this.

If, on the other hand, a typographically identical word (viz.: "place") were to
be defined in this way, and then used in mathematics or physics, it wouldn't be the same
word as the ordinary word "place" upon which the definition itself was
predicated. And, if this new term, "place", is used to define the movement of objects in
DM, then the motion of gross bodies in the material world would still be unaccounted for.

It
could be objected here that it is surely possible to disambiguate the
ordinary word so that it could be employed in a
DM-analysis of motion --, meaning that it was no longer confused with the less precise phrase
"general location".

Since this has yet to be done (even by DM-advocates, who, up until now, have shown that they
aren't even aware of
this problem!) it remains to be seen whether this promissory note is
redeemable. However, even if it were, it would still be of little
help. As we have seen, and will see again, the word "place" (even as
it is used in mathematics) is
itself ambiguous, and necessarily so. [There is more on this in Note 25.]

Moreover, Engels's account requires motion to be depicted by a
continuous variable, while one or both of time or place is/are held to be
discrete, otherwise a contradiction wouldn't emerge (which is, of course,
something even Hegel recognised). This trick is accomplished
either by (1) The simple expedient of ignoring examples of
discrete forms ofmotion (several of which are given below -- this
material from Essay Five has been omitted -- RL), and/or
by (2) Failing to consider
instances where both time and place are continuous -- all the while
imagining that the relevant ordinary words used to depict both have been employed
in their usual senses, and haven't been altered by these new uses/contexts.

Even assuming a stricter
sense of "place" could be cobbled-together somehow, it would still
be of little help. That is because it would either make motion itself impossible --
or, if possible, incomprehensible -- since, given Engels's account, a moving
object would have to be everywhere if it is anywhere, and, it wouldn't
so much move as expand or stretch, as noted earlier.

So, my
argument isn't about tins of beans as such (that was my way of
simplifying the above rather complex arguments so that novices could
appreciate the point), but about what Hegel, Engels or
Lenin could possibly have meant by their use of such language. Unfortunately,
MLT is absolutely no help in this regard. Indeed,
from what little he has
said about locations and points, for example, he is perhaps even more confused than
Engels!

5) It's a
little rich of MLT asserting that I am playing "word games" here, when Hegel
and Engels's argument is precisely just this, a word-game! Both of them attempt to derive what
seem to them to be fundamental theses about every instance of motion in the
entire universe, for all of time, based on what they took to be the 'real'
meaning of a handful of words, none of which they defined clearly (or at all)!
They offer no evidence in support of these odd ideas.

In which case, MLT has no valid reason to cavil if I use language to expose such sloppy
thought.

Indeed, as George
Novack pointed out:

"A consistent materialism can't proceed from
principles which are validated by appeal to abstract reason, intuition,
self-evidence or some other subjective or purely theoretical source. Idealisms
may do this. But the materialist philosophy has to be based upon evidence taken
from objective material sources and verified by demonstration in practice...."
[Novack (1965), p.17. Bold emphasis added.]